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Let A={1,-1,I,-i} hbe the set of four 4th roots of unity prepare the commposition table for multiplication on A and show that ltrbgt (i) A is closed for multiplication (ii) multiplication isassociative on A (iii) multiplication is commutative on A (iv) 1 is the multiplicative identity (v) every element in A has its multiplicative iverse |
Answer» Solution :We MAY PREPAR the composition table for multiplication on A as GIVEN below Clerly 1 is the identity ELEMENT `(1)^(-1)=1(-1)^(-1)=-1(i)^*(-1)=- and (-i)^(-1)=i` |
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